Supercoset construction of Yang-Baxter deformed AdS$_5\times$S$^5$ backgrounds

Understand

We proceed to study Yang-Baxter deformations of the AdS$_5\times$S$^5$ superstring with the classical Yang-Baxter equation.

• We make a general argument on the supercoset construction and present the master formula to describe the dilaton in terms of classical $r$-matrices.
• The supercoset construction is explicitly performed for some classical $r$-matrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived.
• Within the class of abelian $r$-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, $\gamma$-deformations of S$^5$ and Schr\"odinger spacetimes.